Motility-Driven Viscoelastic Control of Tissue Morphology in Presomitic Mesoderm

TL;DR

This work develops a motile vertex-model framework to connect cell-scale motility and active rearrangements with emergent tissue viscoelasticity in the presomitic mesoderm. By validating against PSM explant relaxation dynamics, the authors extract intrinsic mechanical timescales and show motility-driven shifts between elastic and viscous behavior, including persistent residual stress in low-motility regions. Under spatially patterned pulsatile forcing, the tissue acts as a wavelength-selective mechanical filter, with long-wavelength perturbations accumulating into lasting morphologies while short-wavelength fluctuations are dissipated, a scaling governed by motility through $\hat{u}_n(k_0,\mathcal{M}) \sim \frac{\mathcal{M}}{k_0^2}$. The analytical treatment with a two-time-scale viscoelastic model is validated by vertex-model simulations, and localized motility hotspots can drive protrusive, limb-bud-like deformations. Overall, the study provides a mechanistic framework linking motility, viscoelastic memory, and pattern formation in embryonic tissues, with implications for how rhythmic mechanical cues shape morphogenesis and how signaling pathways like FGF tune tissue mechanics.

Abstract

Embryonic tissues deform across broad spatial and temporal scales and relax stress through active rearrangements. A quantitative link between cell-scale activity, spatial forcing, and emergent tissue-scale mechanics remains incomplete. Here, we use a vertex-based tissue model with active force fluctuations to study how motility controls viscoelastic response. After validation against experimental presomitic mesoderm relaxation dynamics, we extract intrinsic mechanical timescales using stress relaxation and oscillatory shear. The model captures motility-dependent shifts between elastic and viscous behavior and the coexistence of fast relaxation with long-lived residual stress. When subjected to spatially patterned, temporally pulsed forcing, tissues behave as mechanical filters: long-wavelength inputs are accumulated, whereas short-wavelength, cell-scale perturbations are rapidly erased, largely independent of motility. Simulations with localized motility hotspots, motivated by spatially confined FGF signaling reported in vertebrate limb development, produce sustained protrusive tissue deformations consistent with experimentally observed early bud-like morphologies. Together, these results establish a minimal framework linking motility-driven activity to wavelength-selective mechanical memory and emergent tissue patterning.

Figures (8)

• Figure 1: Effect of motility in presomitic mesoderm (PSM) rheology and relaxation. (a) Change in the shape of the PSM explant over time. Cell motility gradient drives pear-like shape formation of the explant (Experimental image is taken with permission from MICHAUT2025). (b) A numerical simulation of the vertex model with a gradient in random cell motility in the form of exponential decay benazerafRandomCellMotility2010 from the posterior to anterior tissue has been introduced. The model qualitatively reproduces the experimental observation shown in (a). (c) Examples of rounding of anterior and posterior explants from PSM (image taken with permission from MICHAUT2025). The Anterior and posterior parts show significant distinction in rounding timescales, suggesting variation in viscosity along the A-P axis. (d) Numerical simulation of the vertex model of rounding of tissue from three different regions, anterior (blue), middle (green), and posterior (red) of the model PSM tissue. A higher cell motility results in faster rounding. (e) Time evolution of circularity of the tissue with three different motility values (as in (d)). (f) Time evolution of overlap function $Q(t)$ (see Equation \ref{['eqn:Qt']}). It shows the rate of radial movement of a cell from its initial position. The dotted line marks when $Q(t)$ drops below $1/e$ of its initial value. (g) Dependence of viscosity $\eta$, calculated from the Green-Kubo relation (see S.I. Sec. \ref{['sec:green-kubo']} for definition), and $\alpha$ relaxation Time $\tau_{\alpha}$ on motility. The anterior region shows a high value of viscous timescales, which decreases towards the posterior direction.
• Figure 2: Tissue rheology under standard mechanical protocols. (a) Stress relaxation response for tissues with different motility levels. The decay of shear stress $\sigma_{xy}(t)$ is shown following a step shear deformation. Higher motility leads to faster stress relaxation and lower residual stress. Inset: Long-time behavior of $\sigma_{xy}$ reveals a nonzero plateau, indicating residual stress retention. (b) Relaxation timescale $\tau_\mathrm{s}$ decreases with increasing motility, indicating enhanced fluidization. (c) Residual stress as a function of motility. More motile tissues retain less stress over time. (d) Frequency-dependent storage modulus $G'$ and loss modulus $G"$. At low frequencies, viscous behavior dominates ($G" > G'$); at higher frequencies, the tissue responds more elastically. (e) The loss tangent $\tan{\delta} = G"/G'$ as a function of driving frequency $\omega_0$, illustrating the transition from viscous to elastic dominance. (f) Viscoelastic crossover time of the tissue($\tau_V$), defined by the crossover frequency where $G' = G"$. $\tau_V$ shifts to lower values with increasing motility, reflecting faster stress relaxation dynamics in more active tissues.
• Figure 3: Tissue morphology under temporally pulsatile, spatially sinusoidal perturbations. (a) Schematic of the analytical framework. (I) Synthetic tissue used from the vertex model. (II) Continuum representation of the tissue as a 2D viscoelastic material, modeled as a dashpot (viscosity $\eta_1$) in series with a Kelvin–Voigt element (dashpot with viscosity $\eta_2$ in parallel with a spring of elasticity $E$). (III) Generic time profile of the external forcing: the force remains on for a duration $\mathrm{T_{on}}$ and off for a period $\mathrm{T_{off}}$. (b) Comparison of characteristic timescales extracted from structural relaxation dynamics ($\tau_{\alpha}$) and standard rheological protocols ($\tau_s$ and $\tau_V$) along the anterior–posterior (A–P) axis of the PSM. (c) Morphological outcomes of the vertex-model tissue under pulsatile forcing. (I) Low motility with long-wavelength perturbations ($\sim L_y/4$, where $L_y$ is tissue length along $y$) produces negligible morphological adaptation, but bulk rotation arises from force asymmetry. (II) Intermediate motility with the same wavelength induces moderate adaptation. (III) High motility yields pronounced morphological adaptation. (IV) Shorter-wavelength perturbations ($\sim L_y/16$) fail to elicit significant adaptation or rotation. (V, VI) No morphological adaptation is observed. (d) Analytical predictions versus simulations of long-time tissue morphology in Fourier space, $\hat{u}_{n}(k_0, \mathcal{M})$, as a function of motility $\mathcal{M}$ and wavenumber $k_0$. Here $n$ is the number of on-off cycles. $n\gg1$ is chosen. (I) Predicted deformation increases linearly with motility, in quantitative agreement with simulations. (II) Theory predicts a power-law decay of deformation with increasing wavenumber, matching the simulation findings.
• Figure 4: Effect of FGF signaling on vertebrate limb formation. (a) Chick embryo (adapted with permission from Ohuchi et al. ohuchiMesenchymalFactorFGF101997): (I) Weak Fgf10 expression in the prospective forelimb mesoderm (arrowheads) is seen around 13 Hamburger and Hamilton (HH) stage. (II) Fgf10 expression in the head region and prospective limb mesoderm (arrowheads) increases at around the 16 HH stage. Suggesting Fgf10 plays a key role in limb bud formation. (III) Induction of an ectopic leg-like limb (arrow) following implantation of FGF10-expressing cells in the interlimb region. (b) Zebrafish embryo (adapted with permission from Fischer et al. fischerZebrafishFgf24Mutant2003): (I) Wild-type larva at 3 dpf with pectoral fins protruding from the flanks. (II) ika mutant (Fgf24-deficient) larva lacking pectoral fins (asterisks). (c) Mouse embryo (adapted with permission from Min et al.minFgf10RequiredBoth1998): lateral views of Fgf10$^{+/+}$, Fgf10$^{+/-}$, and Fgf10$^{-/-}$ embryos, showing complete limb absence in the knockout. (d) Simulations using active vertex model tissue to examine the role of FGF-induced motility in limb bud initiation. Starting from an initially compressed configuration, four localized motility hotspots (I) trigger protrusive outgrowths (II), which grow further resembling early limb bud formation (III). The colorbar represents motility value normalised with the maximum used for the posterior PSM.
• Figure S1: (a) A representative epithelial tissue configuration obtained from vertex model simulations. (b) Schematic illustration of a T1 transition involving neighbor exchange. (c) Schematic of a T2 transition representing cell extrusion.